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If the chord joining points `P(alpha)a n dQ(beta)` on the ellipse `((x^2)/(a^2))+((y^2)/(b^2))=1` subtends a right angle at the vertex `A(a ,0),` then prove that `tan(a/2)tan(beta/2)=-(b^2)/(a^2)dot`

A

`a^(2) //b^(2)`

B

`-a^(2) //b^(2)`

C

`b^(2) // a^(2)`

D

`-b^(2)//a^(2)`

Text Solution

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The correct Answer is:
D
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OBJECTIVE RD SHARMA-ELLIPSE-Chapter Test
  1. If (-4, 3) and (8, 3) are the vertices of an ellipse whose eccentricit...

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  2. The area of the triangle formed by three points on the ellipse x^2/a^2...

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  3. If the chord joining points P(alpha)a n dQ(beta) on the ellipse ((x...

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  4. If P(alpha,beta) is appoint on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=...

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  5. The tangent at any point P on the ellipse meets the tangents at the ve...

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  6. P is a point on the circle x^(2) + y^(2) = c^(2). The locus of the mid...

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  7. The locus of the poles of normal chords of the ellipse x^(2)/a^(2) + y...

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  8. The locus of mid-points of a focal chord of the ellipse x^2/a^2+y^2/b^...

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  9. The locus of points whose polars with respect to the ellipse x^(2)/a^(...

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  10. if the chord of contact of tangents from a point P to the hyperbola x...

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  11. The locus of the poles of tangents to the auxiliary circle with respec...

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  12. The locus of the poles of tangents to the director circle of the ellip...

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  13. P is a point on the circle x^(2) + y^(2) = c^(2). The locus of the mid...

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  14. If the tangent to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 makes inte...

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  15. If the tangents to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 make angles a...

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  16. If C is centre of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 and the no...

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  17. If the normals at P(theta) and Q(pi/2+theta) to the ellipse (x^2)/(a^2...

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  18. If a tangent to the ellipse x^2/a^2+y^2/b^2=1, whose centre is C, me...

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  19. The tangent at point P on the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 cu...

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  20. If the lengths of major and semi-minor axes of an ellipse are 4 and sq...

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